Davis suffered the injury in the team's 106-101 win against the Utah Jazz on Wednesday.
He underwent X-rays that night at Crypto.com Arena that revealed no fracture, according to the team, but an MRI Thursday revealed the sprain.
The Lakers said team doctors will reevaluate the star big man in four weeks.
Davis was hurt when he went airborne to catch a lob pass from Malik Monk and came down on Rudy Gobert's heel in the second quarter. Davis' right ankle turned outward and he fell to the floor, clutching the lower leg in pain.
Lakers star LeBron James said Davis left the arena on crutches, and sources told ESPN at the time that Davis experienced significant swelling in the ankle immediately following the injury.
It marks another tough injury break for Davis, who already had missed 17 straight games from late December to late January with a sprained MCL in his left knee.
The Lakers entered Thursday ninth in the Western Conference at 27-31, six games behind the Denver Nuggets, who are No. 6 -- the spot they would have to capture to avoid the play-in tournament. L.A. is four games ahead of the No. 11 New Orleans Pelicans, whom they'll have to stave off to guarantee at least the play-in spot.
After the All-Star break, the Lakers have two games left in February, then play nine games through March 18 -- which would mark about when Davis would be reevaluated.
ESPN's Dave McMenamin contributed to this report.